ON STEPS OF SOLUBILITY OF LATTICES AND DEGREES OF IDEMPOTENCY OF PREVARIETIES OF LATTICES
V. B. Lender · Mathematics of the USSR-Sbornik · 1974
Let be a sub-prevariety of a fixed prevariety (residually closed class) . The smallest ordinal number such that an algebra is -step -soluble is called the step of -solubility of . The smallest ordinal number such that there exists an -step -soluble algebra is called the degree of idempotency of relative to . In the paper is taken to be the class of all lattices, and all ordinal numbers that can be degrees of idempotency of prevarieties of lattices are found. Further, a description is given, depending on the degree of idempotency of a prevariety , of the ordinal numbers that can be steps of -solubility of suitable lattices.Bibliography: 11 items.